Satisfaction and Friendliness Relations within Classical Logic: Proof-Theoretic Approach

摘要

We present the logical friendliness relation in a proof-theoretic fashion as sequent system F. Then, the completeness theorem is proved. On the way to this theorem, we characterize the notion of satisfiability with respect to the classical two-valued semantics, in a proof-theoretic manner as system S, so that the latter becomes part of the definition of system F. Also, we obtain the strong compactness property for friendliness as a corollary of our completeness theorem.